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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 133584v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 133584.dd2 | 133584v1 | \([0, 1, 0, -44568, -52678188]\) | \(-1349232625/164333367\) | \(-1192454487965233152\) | \([2]\) | \(1228800\) | \(2.1480\) | \(\Gamma_0(N)\)-optimal |
| 133584.dd1 | 133584v2 | \([0, 1, 0, -2396808, -1417918284]\) | \(209849322390625/1882056627\) | \(13656793580276723712\) | \([2]\) | \(2457600\) | \(2.4946\) |
Rank
sage: E.rank()
The elliptic curves in class 133584v have rank \(0\).
Complex multiplication
The elliptic curves in class 133584v do not have complex multiplication.Modular form 133584.2.a.v
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
